The equation $$z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0$$ represents a circle of radius

Let z be a complex number such that the principal value of argument, arg z > 0. Then, arg z $$-$$ arg($$-$$ z) is

The general value of the real angle $$\theta$$, which satisfies the equation, $$(\cos \theta + i\sin \theta )(\cos 2\theta + i\sin 2\theta )...(\cos n\theta + i\sin n\theta ) = 1$$ is given by, (assuming k is an integer)

For any non-zero complex number z, the minimum value of | z | + | z $$-$$ 1 | is